Related papers: Axiomatic Music Theory
Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X, in relation with the definability of types.
The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…
It is proposed here that all successful and complete theories always proceed through an intermediate stage of instrumentalism to the final stage of realism. Examples from history of science (both classical and modern) in support of this…
We take a formal approach to the explainability problem of machine learning systems. We argue against the practice of interpreting black-box models via attributing scores to input components due to inherently conflicting goals of…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
This text offers a personal and very subjective view on the current situation of Music Information Research (MIR). Motivated by the desire to build systems with a somewhat deeper understanding of music than the ones we currently have, I try…
A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspects of cosmology that benefit from the…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Several complementary approaches to investigate knotted solutions of Maxwell's equations in vacuum are now available in literature. However, only partial results towards a unified description of them have been achieved. This is potentially…
The development of artificial intelligent composition has resulted in the increasing popularity of machine-generated pieces, with frequent copyright disputes consequently emerging. There is an insufficient amount of research on the…
We develop an abstract axiomatic theory of tie-breaking. A tie-breaking input consists of a finite set N of players, a weak order on N representing the standings to be refined, and an auxiliary information item drawn from a set on which the…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
The determination of musical key is a fundamental aspect of music theory and perception, providing a harmonic context for melodies and chord progressions. Automating this process, known as automatic key detection, is a significant task in…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.